## Abstract

This paper studies the question of how to define, construct, and use obfuscators for probabilistic programs. Such obfuscators compil a possibly randomized program into a deterministic one, which achieves computationally indistinguishable behavior from the original program as long as it is run on each input at most once. For obfuscation, we propose a notion that extends indistinguishability obfuscation to probabilistic circuits: It should be hard to distinguish between the obfuscations of any two circuits whose output distributions at each input are computationally indistinguishable, possibly in presence of some auxiliary input. We call the resulting notion probabilistic indistinguishability obfuscation (pIO). We define several variants of pIO, and study relations among them. Moreover, we give a construction of one of our variants, called X-pIO, from sub-exponentially hard indistinguishability obfuscation (for deterministic circuits) and one-way functions. We then move on to show a number of applications of pIO. In particular, we first give a general and natural methodology to achieve fully homomorphic encryption (FHE) from variants of pIO and of semantically secure encryption schemes. In particular, one instantiation leads to FHE from any X-pIO obfuscator and any re-randomizable encryption scheme that’s slightly super-polynomially secure. We note that this constitutes the first construction of full-fledged FHE that does not rely on encryption with circular security. Moreover, assuming sub-exponentially secure puncturable PRFs computable in NC^{1}, sub-exponentially-secure indistinguishability obfuscation for (deterministic) NC^{1} circuits can be bootstrapped to obtain indistinguishability obfuscation for arbitrary (deterministic) poly-size circuits (previously such bootstrapping was known only assuming FHE with NC^{1} decryption algorithm).

Original language | English |
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Title of host publication | Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings |

Editors | Yevgeniy Dodis, Jesper Buus Nielsen |

Publisher | Springer Verlag |

Pages | 468-497 |

Number of pages | 30 |

ISBN (Electronic) | 9783662464960 |

DOIs | |

State | Published - 2015 |

Event | 12th Theory of Cryptography Conference, TCC 2015 - Warsaw, Poland Duration: 23 Mar 2015 → 25 Mar 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9015 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 12th Theory of Cryptography Conference, TCC 2015 |
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Country/Territory | Poland |

City | Warsaw |

Period | 23/03/15 → 25/03/15 |

### Funding

Funders | Funder number |
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Israel Science Foundation | 1523/14 |